SO fiddle
Test Fiddle mainly for SO Questions
by Nick Craver
HTML
<link rel="stylesheet" href="http://ajax.googleapis.com/ajax/libs/jqueryui/1.8.4/themes/overcast/jquery-ui.css">
<!--select box-->
<div class="select-div">
<select id="select-pub">
<option value="1">Publisher 1</option>
<option value="2">Publisher 2</option>
<option value="3">Publisher 3</option>
<option value="4">Publisher 4</option>
</select>
</div>
<!--this button needs to append the currently selected text to a list-->
<div class="link-div">
<a class="add-button" href="#" style="width:46px;height:22px;display:block;">Add</a>
</div>
<!--the option text must now populate this unordered list-->
<div id="publisher-results">
<ul>
</ul>
JavaScript
$('.add-button').click(function() {
$('<li />', { text: $('#select-pub :selected').text() })
.appendTo('#publisher-results ul');
});